I prefer Barry Allen as The Flash and never liked that they killed him off in the comics, although I thought his death was handled decently, even though the writer himself didn't agree with the decision. It was just kind of ridiculous to me when they were just going to have Wally West become like a Barry Allen imitation later on, like when they gave him a reporter girlfriend/wife like Barry Allen had, twins like Barry Allen had, a police job and secret identity like Barry Allen had, a Reverse Flash like Barry Allen had, an upped power level like Barry Allen had, etc, they made someone who was already essentially a "mini me" version of Barry Allen to begin with MORE of a Barry Allen imitation, IMO. (It was bad enough he had a miniature origin of Barry's and wore his costume to begin with)

And while I enjoyed the JL/JLU show, The Flash on there is very very far from the Wally West of the comics. The JL/JLU Flash is Wally West in name and appearance only, he has Barry Allen's origin and story arc and story/character elements, he has Barry Allen's place in the JLA, etc....and his personality is closer to that of Impulse's. However I enjoyed the show for what it was, but DC has been known to combine their characters a lot in alternate media.

(They did a similar thing with Hal Jordan and Kyle Rayner in the DCAU, even John Stewart in JL/JLU has many of Hal Jordan's story elements)

Anyway, not many people realize this about the animated shows and consider the animated shows to be the "true" versions when in fact they are not, and will say how they prefer Wally to Barry, Kyle to Hal, etc, when the reasons they prefer those characters are because they elements they perceive to belong to them that they like actually belong to Barry Allen and Hal Jordan, so in actuality they would prefer Barry Allen and Hal Jordan, but they just don't know it because they are unfamiliar with them and are unable to recognize their story elements being placed within Wally West and Kyle Rayner (and even John Stewart).

So that is why I prefer Barry Allen pretty much for one thing. He is the original as far as The Flash as we know him is concerned ("iconic" version), and he is the best, IMO.

Anyway, any dynamic you get with Wally Flash in the JL/JLU show, you can just as easily also get with Barry Allen as The Flash. The dynamic is pretty interchangeable as the JL/JLU Flash didn't mirror his comic counterpart much.